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There is a list of various analytical aquifer and gas cap models which are normally based on the relations:

Gas Cap Expansion @model Aquifer drive @model


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Q^{\downarrow}_{GC}(t) = F_{GC}(p(t))



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Q^{\downarrow}_{AQ}(t) = F_{AQ}(p(t))



Variations

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In some specific cases equation 

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can be explicitly integrated:

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